Field of the Invention
The present invention is directed to systems and methods for providing mathematical regression analysis. More specifically, the present invention provides methods and systems for providing mathematical regression analysis in situations where exact feedback on desired output values is difficult or impossible to obtain.
Background Information
Mathematical regression is a method for estimating the value of a set of dependent variables given a set of independent variables. Regression proceeds by having a user or system supply desired values for a large set of samples and an optimization method is utilized to train a regression model using a loss function. In traditional regression, the desired dependent output values provided are exact and do not change during the regression process.
It is frequently the case that it is difficult or impossible for a user or system to supply the exact desired dependent output variables. This can be because giving feedback is expensive in terms of time, effort, money or some other resource; a user or system cannot reliably give good values; or, the correct values are ambiguous (for example, the values are only relative and multiple different sets of values are equally valid).
In such cases, however, a supervising user or system, when given a set of possible values, may improve and potentially correct a subset of these values (i.e. the subset that is obviously wrong). In addition, it may also be possible for a supervising user or system to compare between two sets of possible regression values and determine which one is better.
Accordingly, there is a need for improved methods for providing mathematical regression analysis in situations where feedback is particularly difficult or impossible to obtain.